If we start thinking in the scale of thousands of years, I could very well imagine using this much energy, if we get some nice automated self-sustaining expansion going.

Robots that build solar panels (and more robots) from raw materials they gather, powered by energy they themselves are helping to create. It would be like sending a virus out, no need for any intervention once you get the process going.

They would go out and convert everything into whatever we need. In 2500 years they could even reach other stars.